Integrable Trotterization: local conservation laws and boundary driving

Vanicat, Matthieu (avtor), Zadnik, Lenart (avtor), Prosen, Tomaž (avtor)

We discuss a general procedure to construct an integrable real–time trotterization of interacting lattice models. As an illustrative example we consider a spin-1/2 chain, with continuous time dynamics described by the isotropic (XXX) Heisenberg Hamiltonian. For periodic boundary conditions local conservation laws are derived from an inhomogeneous transfer matrix and a boost operator is constructed. In the continuous time limit these local charges reduce to the known integrals of motion of the Heisenberg chain. In a simple Kraus representation we also examine the nonequilibrium setting, where our integrable cellular automaton is driven by stochastic processes at the boundaries. We show explicitly, how an exact nonequilibrium steady state density matrix can be written in terms of a staggered matrix product ansatz. This simple trotterization scheme, in particular in the open system framework, could prove to be a useful tool for experimental simulations of the lattice models in terms of trapped ion and atom optics setups.

• Jezik: Angleški jezik
• Ključne besede: quantum mechanics
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Leto izida: 2018
• Št. strani: Str. 030606-1-030606-6
• Številčenje: Vol. 121, iss. 3
• PID: 20.500.12556/RUL-106189
• UDK: 530.145
• ISSN pri članku: 0031-9007
• DOI: 10.1103/PhysRevLett.121.030606
• COBISS.SI-ID: 3289700
• Datum objave v RUL: 07.02.2019

VANICAT, Matthieu, ZADNIK, Lenart in PROSEN, Tomaž, 2018, Integrable Trotterization: local conservation laws and boundary driving. Physical review letters [na spletu]. 2018. Vol. 121, no. 3, p. 030606-1- 030606–6. [Dostopano 8 april 2025]. DOI 10.1103/PhysRevLett.121.030606. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=106189

Gradivo je del revije

• Naslov: Physical review letters
• Skrajšan naslov: Phys. rev. lett.
• Založnik: American Physical Society
• ISSN: 0031-9007
• COBISS.SI-ID: 1282575

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: kvantna mehanika

Projekti

• Financer: EC - European Commission
• Program financ.: H2020
• Številka projekta: 694544
• Naslov: Open many-body non-equilibrium systems
• Akronim: OMNES